GPS uses satellites in space to locate objects on earth. With GPS, signals from the satellites arrive at a GPS receiver and are used to determine the position of the GPS receiver. Currently, two types of GPS measurements corresponding to each correlator channel with a locked GPS satellite signal are available for civilian GPS receivers. The two types of GPS measurements are pseudorange, and integrated carrier phase for two carrier signals, L1 and L2, with frequencies of 1.5754 GHz and 1.2276 GHz, or wavelengths of 0.1903 m and 0.2442 m, respectively. The pseudorange measurement (or code measurement) is a basic GPS observable that all types of GPS receivers can make. It utilizes the C/A or P codes modulated onto the carrier signals. The measurement records the apparent time taken for the relevant code to travel from the satellite to the receiver, i.e., the time the signal arrives at the receiver according to the receiver clock minus the time the signal left the satellite according to the satellite clock. The carrier phase measurement is obtained by integrating a reconstructed carrier of the signal as it arrives at the receiver. Thus, the carrier phase measurement is also a measure of a transit time difference as determined by the time the signal left the satellite according to the satellite clock and the time it arrives at the receiver according to the receiver clock. However, because an initial number of whole cycles in transit between the satellite and the receiver when the receiver starts tracking the carrier phase of the signal is usually not known, the transit time difference may be in error by multiple carrier cycles, i.e., there is a whole-cycle ambiguity in the carrier phase measurement.
With the GPS measurements available, the range or distance between a GPS receiver and each of a multitude of satellites is calculated by multiplying a signal's travel time by the speed of light. These ranges are usually referred to as pseudoranges (false ranges) because the receiver clock generally has a significant time error which causes a common bias in the measured range. This common bias from receiver clock error is solved for along with the position coordinates of the receiver as part of the normal navigation computation. Various other factors can also lead to errors or noise in the calculated range, including ephemeris error, satellite clock timing error, atmospheric effects, receiver noise and multipath error. With standalone GPS navigation, where a user with a GPS receiver obtains code and/or carrier-phase ranges with respect to a plurality of satellites in view, without consulting with any reference station, the user is very limited in ways to reduce the errors or noises in the ranges.
To eliminate or reduce these errors, differential operations are typically used in GPS applications. Differential GPS (DGPS) operations typically involve a base reference GPS receiver, a user GPS receiver, and a communication mechanism between the user and reference receivers. The reference receiver is placed at a known location and the known position is used to generate corrections associated with some or all of the above error factors. The corrections are supplied to the user receiver and the user receiver then uses the corrections to appropriately correct its computed position. The corrections can be in the form of corrections to the reference receiver position determined at the reference site or in the form of corrections to the specific GPS satellite clock and/or orbit. Corrections to the reference receiver position are not as flexible as GPS satellite clock or orbit corrections because, for optimum accuracy, they require that the same satellites be observed by the user receiver and the reference receiver.
The fundamental concept of Differential GPS (DGPS) is to take advantage of the spatial and temporal correlations of the errors inherent in the GPS measurements to cancel the noise factors in the pseudorange and/or carrier phase measurements resulting from these error factors. However, while the GPS satellite clock timing error, which appears as a bias on the pseudorange or carrier phase measurement, is perfectly correlated between the reference receiver and the user receiver, most of the other error factors are either not correlated or the correlation diminishes in wide-area applications, i.e., when the distance between the reference and user receivers becomes large.
To overcome the inaccuracy of the DGPS system in wide-area applications, various wide area DGPS (WADGPS) techniques have been developed. The WADGPS includes a network of multiple reference stations in communication with a computational center or hub. Error corrections are computed at the hub based upon the known locations of the reference stations and the measurements taken by them. The computed error corrections are then transmitted to users via a communication link such as satellite, phone, or radio. By using multiple reference stations, WADGPS provides more accurate estimates of the error corrections.
Thus, a user with a GPS receiver may use different modes of navigation, i.e., standalone GPS, DGPS, WADGPS, carrier-phase DGPS, etc. Whichever of the navigation modes is used, there is always the possibility that the range with respect to a satellite are computed based on a faulty measurement, such as a measurement with respect to a failed satellite. When this range is used in determining the position of the user, an erroneous or wrong position would result. Thus, a faulty measurement can cause serious degradation to the reliability and integrity of the GPS system. Therefore, various integrity monitoring techniques have been developed for fault detection and elimination (FDE) in GPS systems. Receiver autonomous integrity monitoring (RAIM) is the name coined by the FAA for methods of integrity monitoring in GPS using redundant GPS satellite measurements.
The literature on RAIM and FDE procedures is extensive. Most of the procedures in the literature, however, are related to aviation use and attempt to bound the probable error in a position domain. As a result, they generally involve very extensive computations. One of the earliest papers describing a RAIM procedure is a paper by Brown and McBurney, “Self-Contained GPS Integrity Check Using Maximum Solution Separation,” Navigation, Vol. 35, No. 1, pp 41-53. In this paper, the authors suggest: (1) obtaining GPS measurements with respect to n satellites in view; (2) for each of the n satellites, solving for the user position based on measurements with respect to the other (n-1) satellites; (3) computing all possible distances between the solutions in the horizontal plane and determining a maximum distance among the possible distances; and (4) using the maximum distance as a test statistic and declaring a failure when the maximum distance exceeds a threshold. Clearly, this technique is very computationally intensive and does not isolate a particular measurement or satellite as being faulty.
Another early paper is by Parkinson and Axelrad, “Autonomous GPS Integrity Monitoring Using the Pseudorange Residual,” Navigation, Vol 35, No. 2, pp 255-271. In this paper, the authors suggest an excellent test statistic based upon pseudorange measurement residuals, but when it comes to using the test statistic to isolate a failed satellite, they use a scheme similar to that used by Brown and McBurney, i.e., for each of a plurality of satellites, they compute a test statistic while leaving out the measurement with respect to the satellite. Again, this procedure presents an excessive computational burden.